Problem: Solve for $x$ : $5x^2 + 55x + 120 = 0$
Answer: Dividing both sides by $5$ gives: $ x^2 + {11}x + {24} = 0 $ The coefficient on the $x$ term is $11$ and the constant term is $24$ , so we need to find two numbers that add up to $11$ and multiply to $24$ The two numbers $3$ and $8$ satisfy both conditions: $ {3} + {8} = {11} $ $ {3} \times {8} = {24} $ $(x + {3}) (x + {8}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x + 3) (x + 8) = 0$ $x + 3 = 0$ or $x + 8 = 0$ Thus, $x = -3$ and $x = -8$ are the solutions.